### Class returning coordinates of iteration maps in a dynamical system

Hi, I'm using sage to study certain rational maps in $1$ dimensional projective space. Specifically I'd like to calculate coordinate maps of $n$-th iteration. I know that there are nth_iterate and nth_iterate_map classes but it seems that nth_iterate class only works on specific points and nth_iterate_map class returns the whole dynamical system, not the coordinate maps. For example, if we define

sage: P.<x,y>=ProjectiveSpace(QQ,1); f=DynamicalSystem([x^2,y^2],domain=P)

then

sage: f.nth_iterate(P[x,y],2)

gives an error that it is unable to convert x to an element of Algebraic Field, and

sage: f.nth_iterate_map(2)

gives a dynamical system as follows.

Dynamical System of Projective Space of dimension 1 over Algebraic Field
Defn: Defined on coordinates by sending (x : y) to
(x^4 : y^4)

What I want is a class, or any method, that returns coordinate maps, probably as a list of maps in $x$ and $y$, of $n$-th iteration. In the previous example, it should return a list $[x^4,y^4]$.
Any help will be appreciated. Thanks in advance!